First make the salsa to give it time to chill: peel the mangoes over a bowl to catch any juice. Cut the flesh away from the stone and dice it into 5 mm (¼ in) cubes. Place the pieces in the bowl with any mango juice and the lime juice.
Stir the chilli into the diced mango along with the coriander and ginger. Add salt and pepper to taste, then cover the bowl and leave the salsa to chill for at least 1 hour to allow all the flavours to develop.
When you are ready to start cooking, place the chicken breasts one at a time between two sheets of cling film and flatten them lightly with a mallet or rolling pin.
Put a ridged, iron grill pan or a heavy-based nonstick frying pan over a high heat. Brush a little oil onto both sides of the chicken breasts, then chargrill or fry them for 4 minutes on each side. The juices must run clear when the breasts are pierced with a knife. Serve them hot with the chilled mango salsa.